Wavelength From Frequency
A television transmitter broadcasts at a frequency of 6.0 × 10⁸ Hz, and a technician must determine the wavelength of the emitted signal in free space.
Select the correct option:
Solution
0.5 m
Grounded in NCERT Class 12, Chapter 8 (Electromagnetic Waves), the wavelength of an electromagnetic wave in free space is obtained from λ = c/f, since all such waves travel at the speed of light c = 3 × 10⁸ m/s. The broadcast signal is a radio-frequency electromagnetic wave that needs no medium to propagate. Substituting the given frequency: λ = (3 × 10⁸)/(6.0 × 10⁸) = 0.5 m, a typical metre-scale wavelength for such transmissions. The value 2.0 m is incorrect because it inverts the ratio, dividing frequency by speed instead of speed by frequency in the wrong sense. The value 18 m arises from multiplying speed and frequency and mishandling powers of ten. The value 0.05 m results from a decimal-place slip, misplacing one power of ten in the division. A magnitude check confirms that a signal near 600 MHz should have a sub-metre wavelength, consistent with the calculated 0.5 m, so that answer is validated.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic waves
- Topic
- wavelength from frequency
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
0.5 m
Grounded in NCERT Class 12, Chapter 8 (Electromagnetic Waves), the wavelength of an electromagnetic wave in free space is obtained from λ = c/f, since all such waves travel at the speed of light c = 3 × 10⁸ m/s. The broadcast signal is a radio-frequency electromagnetic wave that needs no medium to propagate. Substituting the given frequency: λ = (3 × 10⁸)/(6.0 × 10⁸) = 0.5 m, a typical metre-scale wavelength for such transmissions. The value 2.0 m is incorrect because it inverts the ratio, dividing frequency by speed instead of speed by frequency in the wrong sense. The value 18 m arises from multiplying speed and frequency and mishandling powers of ten. The value 0.05 m results from a decimal-place slip, misplacing one power of ten in the division. A magnitude check confirms that a signal near 600 MHz should have a sub-metre wavelength, consistent with the calculated 0.5 m, so that answer is validated.
This easy difficulty physics question is from the chapter electromagnetic waves, covering the topic of wavelength from frequency. It appeared in the 2025 exam.
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